Персона:
Леонов, Александр Сергеевич

Организационные подразделения

Организационная единица

Институт общей профессиональной подготовки (ИОПП)

Миссией Института является: фундаментальная базовая подготовка студентов, необходимая для получения качественного образования на уровне требований международных стандартов; удовлетворение потребностей обучающихся в интеллектуальном, культурном, нравственном развитии и приобретении ими профессиональных знаний; формирование у студентов мотивации и умения учиться; профессиональная ориентация школьников и студентов в избранной области знаний, формирование способностей и навыков профессионального самоопределения и профессионального саморазвития. Основными целями и задачами Института являются: обеспечение высококачественной (фундаментальной) базовой подготовки студентов бакалавриата и специалитета; поддержка и развитие у студентов стремления к осознанному продолжению обучения в институтах (САЕ и др.) и на факультетах Университета; обеспечение преемственности образовательных программ общего среднего и высшего образования; обеспечение высокого качества довузовской подготовки учащихся Предуниверситария и школ-партнеров НИЯУ МИФИ за счет интеграции основного и дополнительного образования; учебно-методическое руководство общеобразовательными кафедрами Института, осуществляющими подготовку бакалавров и специалистов по социо-гуманитарным, общепрофессиональным и естественнонаучным дисциплинам, обеспечение единства требований к базовой подготовке студентов в рамках крупных научно-образовательных направлений (областей знаний).

Фамилия

Леонов

Имя

Александр Сергеевич

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Теперь показываю 1 - 10 из 33

Только метаданные
ON THE PROPERTIES OF A FAST ALGORITHM FOR SOLVING A THREE-DIMENSIONAL INVERSE PROBLEM OF SCALAR ACOUSTICS
(2024) Bakushinsky, A. B.; Leonov, A. S.; Леонов, Александр Сергеевич
Только метаданные
Fast Solution Algorithm for a Three-Dimensional Inverse Multifrequency Problem of Scalar Acoustics with Data in a Cylindrical Domain
(2022) Bakushinskii, A. B.; Leonov, A. S.; Леонов, Александр Сергеевич
© 2021, Pleiades Publishing, Ltd.Abstract: A new algorithm for stable solution of a three-dimensional scalar inverse problem of acoustic sensing of an inhomogeneous medium in a cylindrical domain is proposed. Data for its solution is the complex amplitude of the wave field measured outside the acoustic inhomogeneities in the cylindrical layer. With the help of the Fourier transform and Fourier series, the inverse problem is reduced to a set of one-dimensional Fredholm integral equations of the first kind. Next, the complex amplitude of the wave field is computed in the inhomogeneity region and the desired sonic velocity field is found in this region. When run on a moderate-performance personal computer, the algorithm takes tens of seconds to solve the inverse problem on rather fine three-dimensional grids. The accuracy of the algorithm is analyzed numerically as applied to test inverse problems at different frequencies, and the stability of the algorithm with respect to data perturbations is investigated.
Только метаданные
Phase Analysis of the Activity of a Voice Source
(2021) Sorokin, V. N.; Leonov, A. S.; Леонов, Александр Сергеевич
© 2021, Pleiades Publishing, Ltd.Mathematical models are proposed that make it possible to relate the parameters of a voice source with the parameters of the phase-frequency responses (PFR) of speech signal segments. In particular, it was found that the duration of operation of a source can be found from the average length of the intervals between the zeros and discontinuities of these PFR. For synthetic and real speech signals, based on the established properties of the phase response and the proposed heuristic methods for their analysis, a numerical estimate of the periods of the fundamental tone, the duration of the voice source within these periods, as well as the moments of the beginning Top and end Tcl actions of the voice source. The existence of the upper limit of the frequency range of the fundamental tone F0 within which the estimation error F0 does not exceed 5% is experimentally established. The average error in estimating the duration of a voice source using the proposed method for speech segments from the Arctic database was less than 0.3% for two speakers, and for a third speaker, it was 6.2%. It is shown that the error in determining values Top and Tcl depends on the properties of the voice source and increases significantly for F0 > 220 Hz. The most probable error in estimating quantities Top for three speakers from the Arctic database is estimated as 1.5, 10.2, and 13.5%; for Tcl, it is –9.7, –20.2, and –13.9%.
Только метаданные
Application of M.Riesz potentials for solving a 3D inverse problem of acoustic sounding
(2019) Leonov, A. S.; Леонов, Александр Сергеевич
© 2019 Published under licence by IOP Publishing Ltd.An inverse coefficient problem for time-dependent 3D wave equation is under consideration. We recover a spatially varying coefficient of this equation knowing special time integrals of the wave eld in an observation domain. The inverse problem has applications to the acoustic sounding, medical imaging, etc. We reduce the inverse problem to a new linear 3D Fredholm integral equation of the first kind in which the integral operator has the form of well-known M.Riesz potentials. The equation has a unique solution for a considered class of coefficients. Assuming a special scheme for recording the data of the inverse problem, we present and substantiate a numerical algorithm of solving this integral equation. The algorithm does not require significant computational resources and a long solution time. It is based on the use of fast Fourier transform. Typical results of solving 3D inverse problem in question on a personal computer for simulated data demonstrate high capabilities of the proposed algorithm.
Только метаданные
A posteriori error estimates in linear ill-posed problems
(2026) Leonov, A. S.; Леонов, Александр Сергеевич
Только метаданные
Calculation of the gradient of Tikhonov's functional in solving coefficient inverse problems for linear partial differential equations
(2022) Sharov, A. N.; Yagola, A. G.; Leonov, A. S.; Леонов, Александр Сергеевич
© 2021 Walter de Gruyter GmbH, Berlin/Boston 2021.A fast algorithm for calculating the gradient of the Tikhonov functional is proposed for solving inverse coefficient problems for linear partial differential equations of a general form by the regularization method. The algorithm is designed for problems with discretized differential operators that linearly depend on the desired coefficients. When discretizing the problem and calculating the gradient, it is possible to use the finite element method. As an illustration, we consider the solution of two inverse problems of elastography using the finite element method: finding the distribution of Young's modulus in biological tissue from data on its compression and a similar problem of determining the characteristics of local oncological inclusions, which have a special parametric form.
Только метаданные
Source recovery with a posteriori error estimates in linear partial differential equations
(2020) Leonov, A. S.; Леонов, Александр Сергеевич
© 2020 Walter de Gruyter GmbH, Berlin/Boston 2020.We consider inverse problems of recovering a source term in initial boundary value problems for linear multidimensional partial differential equations (PDEs) of a general form. A universal stable method suitable for solving such inverse problems is proposed. The method allows one to obtain in the same way approximations to exact sources in different kinds of PDEs using various types of linear supplementary conditions specified with an error. The method is suitable for both spacewise dependent and time-dependent sources. The method consists in preliminary calculation of a special matrix introduced in the article, the matrix of the source inverse problem, and then inverting it using Tikhonov regularization. The matrix can be obtained by solving a number of initial boundary value problems in question with sources in the form of basis functions. Having spent some time for preliminary finding the matrix (for example, by finite element method with a sufficiently detailed grid), we can then use this matrix to quickly solve the inverse problem with various data. The same technique can be applied to solve inverse source problems in linear steady-state PDEs. We also propose an a posteriori error estimation method for the obtained approximate solution and give a numerical algorithm for such estimation. In addition, a relationship is established between the posterior estimate and the lower estimate for the optimal accuracy of solving the inverse problem. The proposed method of solving inverse source problems is illustrated by the numerical solution of model examples for one-dimensional and two-dimensional PDEs of different kinds with a posteriori error estimates.
Только метаданные
Piecewise uniform regularization for the inverse problem of microtomography with a-posteriori error estimate
(2020) Wang, Y.; Yagola, A. G.; Leonov, A. S.; Леонов, Александр Сергеевич
© 2018, © 2018 Informa UK Limited, trading as Taylor & Francis Group. An inverse microtomography problem is under consideration in a class of functions with bounded VH variation. An algorithm for solving this problem is proposed based on Tikhonov's regularization with a special regularizer. The algorithm ensures piecewise uniform convergence of approximate solutions to exact solution of the inverse problem. In addition, the question of a-posteriori error estimate of approximate solutions obtained is considered. A new numerical algorithm for finding this estimate is proposed. Numerical experiments on solving a model inverse problem on the class of functions with bounded VH variation are presented along with the results of a-posteriori error estimate for approximate solutions obtained.
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An Algorithm for Improving the Condition Number of Matrices and Its Application for Solving the Inverse Problems of Gravimetry and Magnetometry
(2025) Leonov, A.; Lukyanenko, D.; Yagola, A.; Wang, Y.; Леонов, Александр Сергеевич
Только метаданные
Methods for Solving Ill-Conditioned Systems of Linear Equations That Improve the Conditionality
(2024) Leonov, A. S.; Леонов, Александр Сергеевич